Fill in the values in the table below to give a legitimate p

Solution

for legitimate PDF, the sum of all probabilities must be 1. Here the sum of given probabilities is 0.36, and we need to fill last 2 cells such that total sum is 1, i..e, the sum of last 2 cells should be 0.64

Therefore we could have any pair here (a,b), such that (a+b) = 0.64 and both are non-negative. For this example, we can take a = P(X=5) = 0.32 and b = P(X=6) = 0.32